Question

Find the equation of line through the intersection of lines 2x – y = 1 and 3x + 2y = –9 and making an angle of 30° with positive direction of x-axis.

Answer 1

Since the line passing through the x-axis makes an angle of 30° with the positive direction of the x-axis.

The slope of the line is given by tan `30^circ = 1/sqrt(3)`

The intersection of the lines 2x – y = 1 and 3x + 2y = –9 is given by solving the equation simultaneously. 

So, multiplying equation 2x – y = 1 by 2, we get

4x – 2y = 2 

Now add this resulting to the second equation 3x + 2y = –9

`=>` 7x = –7

`=>` x = –1

Substituting the value of x ∈ 2x – y = 1, we get

y = –3 

Thus, the intersection of the lines is (–1, –3).

To find the equation of the required line,

We use the slope-point form, so we get 

`y - (-3) = 1/sqrt(3)[x - (1)]`

i.e. `y + 3 = 1/sqrt(3)(x + 1)` 

i.e `y = x/sqrt(3) + 1/sqrt(3) - 3`